Genetic data has transformed the field of evolutionary biology. The age of genomics offers the possibility of measuring molecular information in the present and using it to infer evolutionary events from the distant past. The increasing availability of genetic data and computational power offer the challenge and the opportunity to develop improved methods of analysis that are able to use the data fully to further our understanding of molecular evolution. Bayesian approaches to the estimation of phylogeny began in the mid 1990s and are rapidly increasing in popularity. Important advantages of the Bayesian approach include easily interpreted measures of uncertainty and computational feasibility for solutions to highly complex problems. This grant proposal describes an ambitious plan to improve many aspects of the Bayesian approach to phylogeny estimation and to build practical tools capable of analyzing very large genetic data sets. Specific aims of the proposal are to: (1) improve models for evolution of molecular sequences; (2) improve models for genome-scale rearrangement; (3) develop models to combine information from molecular sequences and from genome arrangements; (4) develop methods to handle partial data; (5) improve methods for ancestral sequence estimation; (6) develop methods to elicit informative prior distributions; (7) develop visualization-based interfaces for exploring distributions of phylogeny; (8) develop computational algorithms to apply Bayesian methods to very large phylogenies; and (9) test the robustness of our methods. The proposed research will enhance scientific understanding in an area where there is potential benefit to society, for example, in analysis of rapidly evolving viruses, such as HIV. We will develop powerful new research tools for phylogenetic inference and distribute these tools for free via the web. This proposal provides the opportunity for students in biology, computer science, human-computer interaction, statistics, and computational mathematics to work with each other and the principle investigators on a large cross-disciplinary project that will enrich the education of these students.